The original design work was done by Smyth (2013) who dealt with the design of the rotor. At the full rotor operating point, the difference between the results was only 1.31%.
1 Introduction
Rocket Engines
Another major advantage of liquid propellant rocket engines is the fact that they can be refueled. In the design of the hypothetical launch vehicle, the gas generator cycle was chosen because of its simplicity.
Computational Fluid Dynamics (CFD)
The next phase involves the selection of the physical models that represent the flow characteristics. The initial conditions specify the values of the fluid variables in the entire flow domain at the starting point of a simulation.
2 Literature Review
Mesh Models
The distribution of prism layers is related to the y+ wall value of the model. As stated, the Y+ wall value can be set by determining the thickness of the prism layer closest to the wall.
Turbulence Modeling
- Direct Numerical Simulation
- Detached Eddy Simulation
The K-Omega model provides a more accurate flow prediction than the K-Epsilon model at stronger pressure gradients (De Beristain, 2012). If this cross-diffusion term is included in the K-Omega model, the results are identical to those of the K-Epsilon model.
Previous Research
Bacharoudis, et al., (2008) were concerned with the influence of the outlet blade angle on the performance of a centrifugal pump. Shojaeefard, et al., (2012) looked at the performance of a centrifugal pump when certain geometric characteristics of the pump were changed.
Physics Models
- Travelling bubble cavitation
- Vortex Cavitation
- Cavitation Nuclei
Cavitation can occur in various machines dealing with liquid flow where the pressure drops below the liquid's vapor pressure. When the local static pressure falls below the vapor pressure of the liquid, the liquid may locally flash to vapor. Cavitation can be avoided if the pressure everywhere is kept above the vapor pressure of the operating fluid.
These microscopic bubbles become macrobubbles as the flow passes through a region where the pressure drops below the liquid's saturation pressure. If the fluid pressure decreased slightly, the core would be expected to increase. Despite this, the critical pressure is often taken as the vapor pressure of the liquid.
Cavitation Modelling
Franc explains that in a liquid where there is a large variety of nuclei, usually the pressure at which cavitation will form is taken as the critical pressure of the largest nuclei. Both cavitation and degassing use the same homogenous seed approach in Star CCM+. The main objective of Zhu & Chen (2012) was to further understand the mechanism for the suppression of gap rotor cavitation.
The gap structure fan consists of a regular rotor with a small blade inserted on the suction side of the regular blades. The model is divided into three domains, separated by interfaces at the inlet and outlet locations of the impeller. Zhu and Chen go on to state that the steady state simulation is strongly dependent on the relative location of the thruster and the volute.
Pump Scaling Laws
To reduce the numerical dissipation in the steady and unsteady simulations, the second-order high-resolution scheme and the second-order backward Euler scheme were used separately for the advection and transient terms. As with the majority of the work reviewed, Zhu & Chen (2012) first modeled a steady simulation and a non-cavitating result was used as an initial guess for the transient cavitation case. For the steady simulation, the frozen rotor interface model was used by Zhu and Chen.
Zhu and Chen used a total pressure input and a mass flow output stating that it is often more appropriate for the case that assumes the pump is being drawn from a static reservoir. Zhu and Chen explained that it is difficult to obtain convergent results for steady-state simulation when the pump is operating at part load. The first affinity law ensures that the inlet flow coefficient is kept constant and determines the flow rate (Qb) for the stepped pump.
3 Scaled Down Impeller
CAD preparation
The fluid flow needs a solid representation so that spatial discretization can take place and the fluid is represented by cells defined by the user. Once the solid model was formed, the fan was removed from the domain to create a negative of the solid.
Computational domain
Mesh generation
The tip gap of the model, between the blade edge and the mantle, was only 0.5 mm. Despite the tip aperture having a custom prism layer mesh, the prism layers failed to generate due to the close proximity of the blade wall and reinforcement. There are several factors that determine the formation of the prism layers in Star CCM+.
Other factors were also altered to aid in the formation of the prism layers in the tip gap. In the process, various failed arrangements of the prism layers were generated in the tip gap. The individual prism layer values can be seen in table 3.4 with the scalar scene for the Y+ values in figure 3.13.
Model Development (Physics)
The idea behind these conditions is that they allow the output pressure to be measured, which in turn leads to the production of the pump curve. While they are inside the rotating area of the model, they do not rotate in real life. Regarding the initial conditions of the model, the only parameter initialized was the velocity in the axial direction (usually on the inlet face).
This technique handles the flow from one component to another by changing the frame of reference while maintaining the relative position of the components. This coordinate system was created based on the rotor, with its 'z' axis being the axis of rotation of the rotor. The basic boundary conditions used in the model can be seen from table 3.7.
Steady State Results
Obviously, the convergence of the solution had to be considered before the results could be accepted. Convergence was considered acceptable based on the status of the residual monitor and the stability of the pressure plot. The stability of the pressure graph can be seen in Figure 3.17, which shows that the solution has converged and is stable.
In terms of computation time, each simulation for the final mesh ran at approximately 20 seconds per iteration for 2000 iterations, giving a total time of approximately hours.
12 369 550 cells
- Cavitation Model Development
- Cavitation Model Results
The scalar plot (Figure 3.19) of the pressure on the rotor shows that the pressure around the leading edge is below the vapor pressure of the liquid. Vortices are visible at the exit of the rotor, which are the result of a narrow diffuser without blades. The convection Courant number is the ratio between the physical time step and the time scale of the convection network.
Cavitation forms at the leading edge of the impeller blade and dissipates quickly. The cavitation prediction shows a small portion of the flow exhibiting signs of two-phase flow. Cavitation in this model is generated by the leading edge of the blade as expected.
4 Full sized impeller
- Introduction
- Mesh Generation
- Model Development
- Steady State Results
- Cavitation Model Development
- Cavitation Model Results
The measured output for the mesh study was the static pressure at the outlet plane of the impeller. The majority of the physics models were the same for both full size and scaled impellers. Because of the velocity ramp, the computational cost for a full-size model was far greater than the scaled model.
The cavitation results of the full-size runner had a greater impact on the performance of the runner than in the scale model (Section 3.7). This can be seen in the figures below, which show the presence of two-phase flow at times corresponding to the lowest and highest values of the pressure graph. The level of cavitation at the end of the fifth rotation can be seen in Figure 4.16.
5 Conclusion
Mesh Optimisation
The effect of achieving such a low value was also found to be insignificant when predicting global pump performance. Instead, in the full-scale model, the stretch factor method was used for all mesh configurations and the number of layers was increased until an acceptable Y+ value was obtained. This research has found that wide refinement of the clearance gap between the blade wall and the shroud has little effect on the accuracy of the three-dimensional model.
If anything, the large-scale enhancement of the tip gap has negative consequences for the CFD model, as the computational time for the model increases with the number of cells in the model. Therefore, the increase in computing time is also large, which takes away one of the advantages of computer analysis, i.e. the speed with which results can be obtained. The research also found that reducing the Y+ value of the wall to just 1 did not significantly affect the results of the numerical model.
CFD Results
The pressure output of the full-scale pump decreased by almost 20% when the multiphase flow model was activated. The difference in the behavior of the fans can possibly be attributed to the scaling process. When comparing the geometry of the two fans, it can be seen that the blades on the scaled fan have a smaller wrap angle.
In other words, the full size impeller blades go through 247o, while the scaled impeller blades only wrap 211o around the impeller. Due to the larger wrapping angles in the full-size impeller, the geometric similarity of the model is affected. The experimental results will certainly shed light on the performance of the scaled impeller at high flow rates, where the CFD model struggled to predict the pressure drop with sufficient accuracy.
Future Work
84 Although experimental data were not available for this project, confidence can be gained from the fact that the CFD model was developed based on principles that have been verified (in similar studies) through experimental testing. Visual access to the impeller passage must be obtained to view the vapor bubbles moving through the vane passages. This means that the inserted change must be designed with the viewport in mind.
These can then be compared to the time-stamped scalar scenes of the two-phase flow present in the CFD model. This data would then allow proper validation of the CFD model of the scaled impeller. Once validation of the scaled model is complete, confidence can be placed in the accuracy of the full-scale CFD model and the performance predicted by this numerical analysis.
6 References
Numerical study of the effects of some geometric features of a centrifugal pump impeller pumping a viscous liquid. The design and analysis of a kerosene turbopump for a South African commercial launch vehicle, MSc Dissertation, University of KwaZulu-Natal, Durban, South Africa. A CFD parametric study of geometric variations on the pressure pulsations and performance characteristics of a centrifugal pump.
Design of a Centrifugal Compressor Fan for Micro Gas Turbine Application, MSc Dissertation, University of Stellenbosch, South Africa. Detached Eddy Simulation of Turbulent Flow and Heat Transfer in Turbine Blade Internal Cooling Channels, Ph.D Dissertation, State University, Faculty of Virginia Polytechnic Institute, Virginia.
7 Appendix A Scaled Model Results
